Lim x- 0 x e x -1 1-cos x

lim _ x→ 0 x( e ^ x 1 ) #160; 1 cos x #160; #160; =lim _ x→ 0 x. e ^ x + e ^ x sin x #160; #160; = 10 = ∞ Hence, the an ...

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Existence of Limit

lim x→ 0 x e ...

Question

$lim x \to 0 \frac{x (e^{x} - 1)}{1 - cos x}$

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Solution

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lim x \to 0 \frac{x (e^{x} - 1)}{1 - cos x}

lim x \to 0 \frac{x (e^{x} - 1)}{1 - cos x}

f (x) = ⎧ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎩ \begin{matrix} \frac{(1 - cos 2 x) (3 + cos x)}{x tan a x} & x < 0; \frac{x (e^{x} - 1)}{1 - cos x} & x > 0; \end{matrix}

a

lim x \to 0 f (x)

lim x \to 0 \frac{(\sqrt{(1 - cos x) + \sqrt{(1 - cos x) + \sqrt{(1 - cos x) + . . . . . . \infty}}}) - 1}{x^{2}}

lim x \to 0 \frac{(\sqrt{(1 - cos x) + \sqrt{(1 - cos x) + \sqrt{(1 - cos x) + . . . . . . . . \infty}}}) - 1}{x^{2}}

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